A057940 Number of prime factors of 4^n + 1 (counted with multiplicity).

1, 1, 2, 1, 3, 2, 3, 1, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 4, 2, 6, 3, 5, 3, 7, 3, 6, 3, 3, 4, 5, 2, 6, 4, 7, 5, 5, 4, 10, 3, 5, 5, 5, 4, 11, 2, 4, 3, 6, 6, 9, 2, 4, 6, 7, 5, 8, 3, 7, 6, 6, 4, 10, 2, 10, 7, 6, 4, 8, 4, 6, 7, 5, 2, 14, 4, 9, 5, 4, 4, 10, 4, 6, 8, 11, 4, 8, 3, 4, 8, 11, 4, 9, 5, 10, 4, 9, 8, 12, 6

Offset

1,3

Links

Max Alekseyev, Table of n, a(n) for n = 1..561 (first 531 terms from Amiram Eldar)

S. S. Wagstaff, Jr., The Cunningham Project

Formula

a(n) = A057957(2n) - A057957(n). - T. D. Noe, Jun 19 2003

a(n) = Omega(4^n + 1) = A001222(A052539(n)). - Wesley Ivan Hurt, Jan 28 2014

a(n) = A054992(2*n). - Amiram Eldar, Feb 01 2020

Maple

with(numtheory); A057940:=n->bigomega(4^n + 1); seq(A057940(n), n=1..100); # Wesley Ivan Hurt, Jan 28 2014

Mathematica

Table[PrimeOmega[4^n + 1], {n, 100}] (* Wesley Ivan Hurt, Jan 28 2014 *)

Crossrefs

bigomega(b^n+1): A057934 (b=10), A057935 (b=9), A057936 (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), this sequence (b=4), A057941 (b=3), A054992 (b=2).

Cf. A001222, A052539, A057957, A274903.

Sequence in context: A278573 A108663 A307314 * A097285 A057432 A361942

Adjacent sequences: A057937 A057938 A057939 * A057941 A057942 A057943

Keyword

nonn

Author

Patrick De Geest, Oct 15 2000

Status

approved